Question

In the following figure,

1. if ∠BAD = 96°, find ∠BCD and ∠BFE.
2. Prove that AD is parallel to FE.

Answer 1

i. ABCD is a cyclic quadrilateral

∴ ∠BAD + ∠BCD = 180°

(Pair of opposite angles in a cyclic quadrilateral are supplementary)

`=>` ∠BCD = 180° – 96° = 84°

∴ ∠BCE = 180° – 84° = 96°

Similarly, BCEF is a cyclic quadrilateral

∴ ∠BCE + ∠BFE = 180°

(Pair of opposite angles in a cyclic quadrilateral are supplementary)

 ∴ ∠BFE = 180° – 96° = 84°

ii. Now, ∠BAD + ∠BFE

= 96° + 84°

= 180° 

But these two are interior angles on the same side of a pair of lines AD and FE

∴ AD || FE